Regression Filtering to Improve Radar Signal Statistics: Application to NEXRAD SZ Phase Coded Data

The identification and filtering of ground clutter echoes, thus separating them from weather radar echo, is an ongoing area of research. Most weather radar groups employ a spectral domain technique that typically requires that the time series is first multiplied by an attenuating window function and then the power spectrum is calculated where spectral components around zero velocity are set to zero. A disadvantage of applying a window function to the time series is that it attenuates the accompanying weather signal and thereby eliminates some of the information about the weather signal. This translates to higher measurement standard deviations for the weather signal.
Another known technique for removing ground clutter signal is regression filtering. It is based on the observation that the ground clutter signal varies very slowly in time whereas weather signals generally vary substantially faster. To remove the slowly varying part of the signal, a regression curve (i.e., a polynomial) is fitted to the signal and then subtracted, thus leaving the weather signal intact. The advantage of the regression filter is that no time domain window is required and thus better weather signal statistics are possible. The regression clutter filter (RCF) has been recently investigated and described by Hubbert et al. 2021, Using a Regression Ground Clutter Filter to Improve Weather Radar Signal Statistics: Theory and Simulations, JTECH.

The RCF is a high pass filter. If the trend of the data is of interest, then the regression filter is a low pass filter. To our knowledge, a regression filter has never been used as a band stop filter on finite length times series such a radar data. For example, regression filtering is not useful for band stop (bandpass) filtering, i.e., rejecting (selecting) an arbitrary frequency or a set of frequencies. First, we demonstrate how regression can accomplish band stop filtering. This is accomplished without the use of a window function and it avoids filter warmup issues that plague FIR and IIR filters especially for short length data such as radar time series.

SZ phase coding is a signal processing technique used by the National Weather Service for separating multiple trip echoes thereby increasing the unambiguous velocity and range for pulse transmission radars. Typically, there is strong trip echo overlaid by weak trip echos. In order to estimate the weak trip velocity, the strong trip echo must be eliminated. To do this, a frequency domain 3/4 spectral notched is typically used. The SZ phase coding technique also requires a time domain window function such as the von Hann. The application of this window function effectively reduces the number of independent samples available for radar variable computation which intern increases the standard measurement error of the retrieved radar variable. In addition, if there is also ground clutter signal present, that too must be filtered. In this paper we show how the regression filter can be used to eliminate both ground clutter and the strong trip echo. The resulting weak trip velocity estimates show a significant improvement over the currently used NEXRAD SZ processing algorithm. Experimental NEXRAD data are given that demonstrate the improved weak trip velocity recovery.